How much is the biggest stack worth in ICM with 3 players left?

Seat 1 holds 10,000 chips, 33.3% of the chips in play, and is worth 33.3% of the prize pool when 2 places pay 65/35 percent. That is +0.00 points against its chip share.

What equity does the smallest stack need to call the biggest stack's all-in?

60.6%. In chips alone the call breaks even at 50%, but the bubble factor of 1.54 raises the requirement because losing costs the smallest stack 33.33% of the prize pool.

Why is ICM equity different from chip share?

Because the prize pool is paid by place, not by chips. Doubling a stack does not double its payout, so each extra chip is worth less than the one before it. Here the biggest stack is worth 33.3% of the prize pool for 33.3% of the chips.

ICM: Even stacks, 3 Players, 2 Paid

In ICM, 10,000 chips out of 3 players is 33.3% of the chips and 33.3% of the prize money when 2 places pay 65/35 percent. The 10,000-chip stack holds 33.3% of the chips and is worth 33.3%.

How much is each stack worth with 3 players left?

The stacks are even stacks: every player holds 10,000 chips. That makes 30,000 chips in play, and two places paid, 65 and 35 percent. The table gives each seat's share of the prize pool next to its share of the chips.

Chips and prize equity with 3 players left, payouts 65/35 percent
Seat	Chips	Share of chips	ICM equity	ICM minus chips
Seat 1	10,000	33.33%	33.33%	+0.00 points
Seat 2	10,000	33.33%	33.33%	+0.00 points
Seat 3	10,000	33.33%	33.33%	+0.00 points

Share of the chips against share of the prize pool

Seat 1Chips 33.3%Prize 33.3%
Seat 2Chips 33.3%Prize 33.3%
Seat 3Chips 33.3%Prize 33.3%

Prize money flattens the stacks. Seat 3 gives up 0.00 points of equity compared with its share of the chips, and Seat 1 gains 0.00 points.

How often does each seat finish in the money?

Before payouts are applied, each stack has a chance of every finishing place. The biggest stack cashes 66.7% of the time, the smallest 66.7%, with 2 places paid.

Chance of finishing in each place
Seat	First	Second	Third	Paid
Seat 1	33.33%	33.33%	33.33%	66.67%
Seat 2	33.33%	33.33%	33.33%	66.67%
Seat 3	33.33%	33.33%	33.33%	66.67%

Where each seat's prize equity comes from, in points of the prize pool
Seat	From first	From second	Total
Seat 1	21.67	11.67	33.33%
Seat 2	21.67	11.67	33.33%
Seat 3	21.67	11.67	33.33%

What is the bubble factor for each seat with 3 players left?

The bubble factor is the prize equity a player loses by losing an all-in divided by the equity gained by winning it. The highest figure here is 1.54, for Seat 1 calling Seat 2, and the lowest is 1.54, for Seat 1 calling Seat 2.

Bubble factor when the row seat calls an all-in from the column seat
Seat	vs Seat 1	vs Seat 2	vs Seat 3
Seat 1	none	1.54	1.54
Seat 2	1.54	none	1.54
Seat 3	1.54	1.54	none

How much equity does a call need?

When the smallest stack (Seat 3) calls an all-in from the biggest (Seat 1), the bubble factor is 1.54. A call that needs 50% in chips needs 60.6% once prize money counts, which is 10.6 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.54 and needs 60.6%, 10.6 points over the chip figure. Here the bigger stack pays the larger premium: losing costs it 33.33% of the prize pool and winning adds 21.67%.

Break-even equity for two all-in calls, risking and winning the same chips
Call	All-in (chips)	Bubble factor	Chip break-even	ICM break-even	Equity now	Equity if win	Equity if lose
Smallest stack calls biggest	10,000	1.5385	50.0%	60.6%	33.33%	55.00%	0.00%
Biggest stack calls smallest	10,000	1.5385	50.0%	60.6%	33.33%	55.00%	0.00%

Where can I compare other stack patterns?

Open a sibling to see how the same payouts value a different split of the chips. For your own stacks and payouts, use the ICM calculator.

How was this ICM table computed?

Each player finishes first with a chance equal to their share of the chips, and every later place is drawn the same way from the players left. Prize equity is the payout of each place times the chance of finishing there. The bubble factor divides the equity lost by losing an all-in by the equity gained by winning it, with the other stacks unchanged, and a player who reaches 0 chips takes the lowest place.

Source: Malmuth-Harville ICM, computed by GeorgeLiPoker's own library. The model follows D. A. Harville, 'Assigning Probabilities to the Outcomes of Multi-Entry Competitions', Journal of the American Statistical Association, 1973.

Questions

How much is the biggest stack worth in ICM with 3 players left?: Seat 1 holds 10,000 chips, 33.3% of the chips in play, and is worth 33.3% of the prize pool when 2 places pay 65/35 percent. That is +0.00 points against its chip share.
What equity does the smallest stack need to call the biggest stack's all-in?: 60.6%. In chips alone the call breaks even at 50%, but the bubble factor of 1.54 raises the requirement because losing costs the smallest stack 33.33% of the prize pool.
Why is ICM equity different from chip share?: Because the prize pool is paid by place, not by chips. Doubling a stack does not double its payout, so each extra chip is worth less than the one before it. Here the biggest stack is worth 33.3% of the prize pool for 33.3% of the chips.